Competing Auctions in Intermediated Markets

Abstract: We analyze competing auctions in intermediated markets, where a seller selects among parallel mechanisms for the sale of a single good, most prominently the relay-and-protocol architecture of proposer-builder separation in Ethereum. When the intermediary can enforce single-homing on its bidders, sealed-bid second-price intermediary auctions fully unravel into the sealed first-price principal auction; open bidding-format intermediaries unravel only partially, collapsing into first-price in equilibrium under symmetric latency and sorting fast bidders to the intermediary under asymmetric latency. Any last-look advantage is removed through the availability of a credible sealed bidding channel. These results extend to multi-plexing environments (no enforcement by the intermediary). While the unraveling result indicates that the availability of a sealed first-price bidding channel pushes the overall market to the same auction structure, the very assumption of the credibility of such channel is problematic, as the seller may have an incentive to leak information: a first-price auction is leakage-resistant in the presence of a single ``fast'' bidder but not against two or more. However, if the seller can credibly commit to not leak bids, it is optimal for them to do so. A main motivation is the forthcoming Glamsterdam update of Ethereum: our analysis suggests that the availability of an in-protocol (first-price) bidding channel severely limits the design space for out-of-protocol auctions by relays and other intermediaries.

• The paper demonstrates that introducing a sealed-bid first-price channel causes second-price intermediated auctions to fully unravel in both single-homing and multi-homing regimes.
• It employs rigorous equilibrium analysis incorporating strategic information leakage, last-look dynamics, and sybil attacks to reveal critical vulnerabilities in auction design.
• The findings imply that credible commitment to sealed-bid protocols consolidates market structures toward first-price mechanisms, influencing Ethereum’s block-building architecture.

Competing Auctions in Intermediated Markets: Formal Analysis and Implications

Overview

The paper "Competing Auctions in Intermediated Markets" (2606.06633) rigorously examines the strategic landscape arising when multiple auction mechanisms, managed by intermediaries, compete to sell a single good on behalf of a principal seller. The analysis centers on blockchain applications, with a strong focus on the proposer-builder separation (PBS) architecture in Ethereum, especially considering the enshrinement of sealed-bid, first-price bidding channels at the protocol layer (ePBS). The work formalizes the unraveling dynamics between competing auction designs, including sealed-bid first- and second-price mechanisms, open bidding with or without last-look, and the effects of strategic information leakage.

Model Structure and Market Institution

The central setting deviates from classical models of competing sellers and instead considers a single good being allocated via parallel and competitive mechanisms (intermediaries/relays), each selecting the highest-revenue bid at the seller’s discretion. Two important participation regimes are defined:

• Single-homing: Bidders can participate in only one channel per auction round, typically enforced by the intermediary.
• Multi-homing (multi-plexing): Bidders can participate simultaneously across multiple channels, possibly exploiting sybil identities.

The study abstracts builder competition as a private-value environment, justified by the current Ethereum block-building pipeline wherein builders derive deterministic value from known bundles and are not performing search themselves.

Core Theoretical Results

Unraveling of Second-Price and Open Auctions

A pivotal result is that the introduction of a credible, sealed-bid, first-price channel causes parallel second-price intermediated auctions to fully unravel in symmetric equilibrium. Specifically, when a first-price auction is available as an outside option, all bidders prefer it, resulting in zero equilibrium participation in second-price channels—both with single-homing (Theorem 1) and, with nuanced argument, in the multi-homing case (Theorem 2).

Propositions further analyze open/English auction formats. In the absence of last-look, the all-English (open relay) equilibrium is unstable in the large-n limit; there exists a threshold $N$ such that for $n \geq N$, English-style relays cannot sustain equilibrium participation (Proposition~\ref{nolastlook}). Under symmetric bidder latency, the open channel collapses toward the first-price form (all bids last and sealed).

Information Leakage and Last-Look Dynamics

The model expands to the strategic disclosure of bid information by the seller/intermediary in the presence of latency asymmetries. When there exists a single fast (privileged) bidder, the first-price auction is leakage-resistant: there is no incentive for the seller to leak bids to the privileged party (Proposition~\ref{1leak}). However, with two or more latency-advantaged bidders, equilibrium behavior incentivizes the seller to leak the highest bid, augmenting rents to the privileged set (Theorem~\ref{2leak}, Proposition~\ref{lastlookrents}), until and unless credible commitment to non-leakage exists.

Crucially, if the seller can ex-ante credibly commit (via technological or institutional means) to a no-leak policy, this is shown to be weakly optimal under standard regularity conditions on the value distribution (Proposition~\ref{prop:commitment_show}). This result is grounded in Myerson’s revenue equivalence and the virtual value calculus.

Sybil Attacks and Protective Strategies

With sybil (pseudo-identity) attacks, bidders can effectively implement first-price strategies within second-price intermediated mechanisms by duplicating their bids, further nullifying the possible strategic diversity that relays can offer.

Implications for Protocol and Market Design

Practically, the analysis indicates that credible, sealed in-protocol first-price bidding channels (as proposed in Ethereum's ePBS upgrade) severely restrict the viable design space for external (off-protocol) intermediaries. Relays operating second-price or open formats are not sustainable against a sealed first-price protocol. This drives consolidation of auction architectures toward first-price mechanisms at the protocol level.

Nevertheless, this consolidation is contingent on the credible sealing of the protocol bid channel. Without cryptographic or reputational assurances against seller bid leakage, the rationale against last-look and open relay bidding weakens, particularly in the presence of multiple fast (potentially colluding) bidders.

Limitations and Extensions

The framework explicitly neglects several axes relevant in practice:

• Collusion: The analysis assumes atomistic, competitive bidders. Collusion opportunities—especially prevalent in permissionless, programmable environments—are not considered.
• Repeated Interaction and Reputation: The static setting precludes sophisticated reputational or commitment games which are relevant for enforcing non-leakage.
• Common-value effects and upstream pipelines: Block builder valuation derivation abstracts away from upstream common-value elements (e.g., searcher dynamics).
• Relay Entry and Format Innovation: The design problem for relays in the presence of these unraveling dynamics is not modeled but is recognized as an open follow-up.

Future Directions

• Enforcement and Commitment Mechanisms: Engineering cryptographically robust sealed channels (e.g., using Trusted Execution Environments) or establishing robust reputation for large staking pools (e.g., Lido) becomes paramount.
• Dynamic Mechanism Design: Modeling repeated interactions could further clarify feasibility of reputation-based commitment to no-leakage equilibria.
• Strategic Relay Entry: Understanding the incentives for relays to offer value-added services (e.g., faster propagation, alternative payment/credit arrangements) in a constrained design space is essential.

Conclusion

This work rigorously demonstrates that in settings where intermediated auctions compete to allocate a single good under parallel mechanisms, the availability of a credible, sealed-bid, first-price channel is structurally dominant. This consolidates equilibrium strategies around first-price mechanisms and collapses the competitive landscape for intermediated second-price or open relay auctions. The theoretical groundwork provided here is directly applicable to the evolution of decentralized block-building markets such as Ethereum’s, informing both protocol upgrades and future research in market design and auction theory.